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The monoenergetic beam of electrons moving along $+ y$ direction enters a region of uniform electric and magnetic fields. If the beam goes straight undeflected, then fields $B$ and $E$ are directed respectively along
$- y$ axis and $- z$ axis
$+ z$ axis and $+ x$ axis
$+ x$ axis and $+ z$ axis
$- x$ axis and $- y$ axis
Solution
The total Lorentz force on the electron is
$\overrightarrow{\mathrm{F}}=-e(\overrightarrow{\mathrm{E}}+\vec{v} \times \overrightarrow{\mathrm{B}})$
The electron will be undeflected if $\mathrm{v} \perp \mathrm{B}.$
If $\mathrm{E}$ is along $+\mathrm{z}$ -direction, the force $-\mathrm{e}$ $\mathrm{E}$ will be along $\mathrm{z}$ -direction. If $\mathrm{B}$ is along $+\mathrm{x}$ direction, force
$-\mathrm{e}(\mathrm{v} \times \mathrm{B})$ will be along $+\mathrm{z}$ divection. When $\mathrm{eE}$ $=$ $\mathrm{evB}.$ the electron moves along $+\mathrm{y}$ -direction undeflected. Hence the correct choice is $(3).$
Thus, for an electron moving along $+$ $\mathrm{y}$ direction. the electric field should be along $+\mathrm{z}$ direction and magnetic field along $+\mathrm{x}$ direction, then the electron will be undeflected.
